# Linear Algebra with NumPy Primer Flashcards

What does this mean?

the set of all real-valued matrices with n rows and d columns

What is this called? What does it mean?

1(x)

- binary indicator function,
- returns 1 if x is a true boolean and 0 otherwise

What does this mean?

the set of all real-valued n-dimensional vectors

What does this mean?

the set of real numbers

What is this?

- A pair of input vector and output scalar
- The superscript indicates the index of this pair, not the exponent. In other words, x(5) is the input vector at index 5, not x raised to the power of 5.

What is this?

|C|

- Determinant if C is a matrix
- Cardinality (number of member elements) if C is a set.

What’s a column vector?

Each entry occupies one row.

What’s this?

One use: denotes the i-th entry of a column vector

What does this mean?

Row vector. Each entry covers 1 column

For matrix A, what is

denotes the i-th row of A

For matrix A, what is

denotes the i-th column of A

What can dot product be applied to? What’s the formula?

Two vectors of same dimensions

What’s the inner product?

Same as dot product

- What can outer product be applied to?
- What does it result in?
- What’s the formula?

- Vectors (can have different number of elements)

What’s another way to express a dot product for two column vectors x and y?

What’s this for two vectors x and y?

The outer product

What’s a matrix-vector product?

- What are the properties of matrix multiplication? (2)
- What properties does it not have? (1)

Matrix multiplication is:

- associative, (AB)C=A(BC)
- distributive, A(B+C)=AB+AC

Is not:

- commutative, AB≠BA

What’s a property of transposes?

What’s the Hadamard product?

elementwise matrix multiplication